Circumcentered Methods Induced by Isometries
Circumcentered Methods Induced by Isometries
复制标题
由等轴测法导出的圆心方法
DOI：
10.1007/s10013-020-00417-z
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发表时间：
2019
影响因子：
0.8
通讯作者：
Xianfu Wang
中科院分区：
文献类型：
--
作者：
Heinz H. Bauschke;Hui Ouyang;Xianfu Wang
受Behling，Bello Cruz和桑托斯最近提出的用于加速Douglas-Rachford方法的外心方法的启发，我们研究了等距诱导的外心映射和外心方法的性质.利用外心映射的半闭性原理，给出了外心等距方法的弱收敛结果，其中包括作为特例的道格拉斯- Rachford方法（DRM）和外心反射方法.我们提供了充分条件的线性收敛的圆周等距/反射方法。我们探索的收敛速度的圆周中心反射方法，考虑所需的迭代次数，以及运行时间作为我们的性能指标。给出了求解线性子空间交线的最佳逼近的环心反射法、DRM法和交替投影法的性能曲线。
Motivated by the circumcentered Douglas–Rachford method recently introduced by Behling, Bello Cruz and Santos to accelerate the Douglas–Rachford method, we study the properness of the circumcenter mapping and the circumcenter method induced by isometries. Applying the demiclosedness principle for circumcenter mappings, we present weak convergence results for circumcentered isometry methods, which include the Douglas– Rachford method (DRM) and circumcentered reflection methods as special instances. We provide sufficient conditions for the linear convergence of circumcentered isometry/reflection methods. We explore the convergence rate of circumcentered reflection methods by considering the required number of iterations and as well as run time as our performance measures. Performance profiles on circumcentered reflection methods, DRM and method of alternating projections for finding the best approximation to the intersection of linear subspaces are presented.
影响因子：
2.2
作者：
Behling, Roger;Bello-Cruz, J.-Yunier;Santos, Luiz-Rafael
通讯作者：
Santos, Luiz-Rafael